Comments by "MC116" (@angelmendez-rivera351) on "Lex Fridman" channel.

  1. Hunter Walker You can still express that using cosines and sines. In fact, using tangents and secants is not necessary for this, because you can use the hyperbolic sine and cosine instead, which are objectively superior functions to work with. Remember that cosh(u)^2 – sinh(u)^2 = 1, so sinh(u)^2 = cosh(u)^2 – 1, or simply sgn(u)sinh(u) = sqrt(cosh(u)^2 – 1). Therefore, to integrate 1/[x·sqrt(x^2 – 1)], let x = cosh(u), so sqrt(x^2 – 1) = sgn(u)sinh(u), and dx = sinh(u)du, so the integrand simplifies to 1/cosh(u) with sgn(u) multiplying from the outside, and this is completely trivial because cosh(u) = [exp(u) + exp(-u)]/2. Grant is correct. The cotangent, secant, and cosecant are not particularly important functions, nor are they the most useful.
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  2. To be fair, most of the memes are subpar and not funny precisely because they are flawed. Good math memes either don't take themselves seriously (so the flaw doesn't matter) or are accurate in some sort of twisted ironic way.
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